badinage vs give-and-take

badinage and give-and-take both are nouns.

Word	Noun	Adjective	Verb	Adverb
badinage	Yes	No	No	No
give-and-take	Yes	No	No	No

As nouns, give-and-take is a hypernym of badinage; that is, give-and-take is a word with a broader meaning than badinage:

Other hypernyms of badinage include backchat, banter, raillery.

badinage (noun)	give-and-take (noun)
frivolous banter	mutual interaction; the activity of reciprocating or exchanging (especially information)
	an exchange of views on some topic
	light teasing repartee